The Magdeburg Thermos Container

A comment from the slacktivist

Sometimes I can’t get the thermos open. This is frustrating because: A) There is coffee in the thermos, and I want coffee; and B) I twisted the thermos lid shut myself, and thus it seems logical to expect that I should also be strong enough to untwist it myself.

Oh, and as for the thermos, I find running hot water over the lid for a bit usually does the trick.

Logic? Nay, it is basic thermodynamics is the problem, and solution, here. A thermos is a good insulator — a vacuum is an excellent barrier against conduction and convection, but it’s not perfect — and you still have radiation. So the coffee cools, and since you likely left an air gap in the container, the pressure of that air is going to drop along with the temperature. PV = nRT. The volume is fixed, and we can assume n is not going to vary too much — the air will likely have 100% relative humidity fairly quickly after the thermos is sealed. As the system cools some small amount will condense, but to first order I’d expect it to be a linear relation. Even a small container with a diameter of 7.5 cm (~3 inches) has a surface area of ~44 cm^2 (7 square inches). For each 1ºC drop in temperature of hot water, that’s about a 0.003 (0.3%) drop in pressure, which is about 1.3 N of force, or 1/3 of a pound. So what of the temperature has dropped 10 degrees? This problem is amplified for larger caps, since it depends on surface area — a 4-inch cap will give you a half a pound per ºC.* On a sealed container with less structural integrity and/or sufficiently large surface area, cooling a liquid/gas mixture inside can lead to the container collapsing.

And it gets worse because the coffee is probably making a good seal of the threads — some air might have escaped when it was closing but now it can’t get in, so now you are trying to increase the volume which causes a further drop in pressure. More work that your hands have to do. This actually is more of a problem when you’ve filled the container up, since the relative change in volume is larger. A container that’s mostly filled with air will see only a small increase in the volume, but one filled with coffee might require that the volume double, meaning the pressure has to drop in half (roughly — water will evaporate at the lower pressure to mitigate this). So this might be responsible for a several percent drop in pressure, corresponding to several pounds of force on the cap.

The net result is that you are pulling against a vacuum (poor quality from a lab perspective, but that’s just a matter of magnitude) This is a version of the Magdeburg hemisphere experiment.

Heating does two things: it increases the pressure inside, and if you are heating the container faster than the cap, the differential expansion can allow some air to get inside to equalize the pressure.

* I really shouldn’t mix units like this, but being from the US I still think of weight and force of everyday events in terms of pounds.